Stability of stochastic differential delay systems with integral/
fragment-integral term and applications
Abstract
This article investigates the stochastic stability of stochastic
differential delay systems (SDDSs) with path information and their
applications in consensus control of multi-agent systems (MASs) based on
the path information feedback. Here, the integral path information and
fragment-integral path information are considered respectively. The mean
square (m.s.) and almost sure (a.s.) exponential stability criteria of
the SDDSs with path integral information are established respectively
according to the two types of path information. It is shown that the
fragment-integral term may work positively for stochastic stability.
Moreover, the obtained stochastic stability theorems are applied to
design a distributed proportional integral/ fragment-integral control
protocol and establish consensus conditions for stochastic MASs under
proportional-integral (PI) -type controls. Finally, the effectiveness of
the results is verified through two simulation examples.